Finite Group Databasebeta

← #25146340

Subgroups — #25146340

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583099C211yesmaximal, characteristic
2C2×#14583030C211yesmaximal, characteristic, complemented
3#19139594C211yesmaximal, characteristic
4#19135980C211yesmaximal, characteristic, complemented
5#19135966C211yesmaximal, characteristic, complemented
6#19135910C211yesmaximal, characteristic, complemented
7#19135910C211yesmaximal, characteristic, complemented
8#19135479C211yesmaximal, characteristic, complemented
9#19135452C211yesmaximal, characteristic, complemented
10#19135418C211yesmaximal, characteristic
11#19135361C211yesmaximal, characteristic, complemented
12#19135291C211yesmaximal, characteristic, complemented
13#19135277C211yesmaximal, characteristic, complemented
14#19134425C211yesmaximal, characteristic, complemented
15C43×#2581C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063322C2211yescharacteristic
19C2×#13063314—21no—
20#14583099—24no—
21#14583030—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×C4⋊(C43⋊C8)C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×C4×C43⋊C8C2211yescharacteristic
38#14582816—21no—
39#14582816—21no—
40#14582801C2211yescharacteristic
41#14582801C2211yescharacteristic
42#14582801C2211yescharacteristic
43#14582801C2211yescharacteristic
44#14582800—21no—
45C4×C4⋊Dic43C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C2×C4×Q8×C43C2211yescharacteristic
51C2×C4×Q8×C43C2211yescharacteristic
52C43×#400—21no—
53C43×#395—21no—
54C43×#391C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#387—21no—
59C43×#387—21no—
60C43×#382C2211yescharacteristic
61C22×D172—21no—
62C22×D172—21no—
63C22×D172C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C2×#10621884—41no—
70C2×#10621884—41no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063322—22no—
76#13063322—22no—
77#13063314—44no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89#13063258—41no—
90#13063256—41no—
91C4⋊(C43⋊C8)—22no—
92C4⋊(C43⋊C8)—22no—
93C4⋊(C43⋊C8)D414yes—
94#13063249—22no—
95#13063249—22no—
96#13063245—22no—
97#13063245—22no—
98#13063245—22no—
99#13063245—22no—
100#13063245—41no—
101#13063245—41no—
102#13063236—22no—
103#13063236—22no—
104C4×C43⋊C8—22no—
105C43⋊#95—21no—
106C22×Q8×C43D411yescharacteristic
107C22×Q8×C43C2311yescharacteristic
108C4×Q8×C43—22no—
109C4×Q8×C43—22no—
110C4×Q8×C43—22no—
111C4×Q8×C43—22no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C4⋊C4×C43D411yescharacteristic
116C2×C4⋊C4×C43D411yescharacteristic
117C2×C4⋊C4×C43D411yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C2×C42×C43C2311yescharacteristic
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133C23×D43—21no—
134C23×D43—21no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
137C2×Q8×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—41no—
143C2×Q8×C43#4112yes—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2411yescharacteristic
155C22×Dic43—21no—
156C22×Dic43—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C2×D172—21no—
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—42no—
170C2×D172—42no—
171C2×D172—42no—
172C2×D172—42no—
173C2×D172—81no—
174C2×D172—81no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—42no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43—42no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—42no—
192C42×C43C2×D412yes—
193C42×C43#4112yes—
194#10621884—44no—
195#10621884—44no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—81no—
201(C2×D43)⋊C4—81no—
202(C2×D43)⋊C4—81no—
203(C2×D43)⋊C4—81no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4×Dic43—42no—
209C2×C43⋊C8—21no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8C2×D412yes—
219C2×C43⋊C8C2×D412yes—
220C2×C43⋊C8#4112yes—
221C23×C43C22×D411yescharacteristic
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C22×D43—41no—
230C22×D43—41no—
231C22×D43—41no—
232C22×D43—41no—
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236Q8×C43—22no—
237Q8×C43—22no—
238Q8×C43—44no—
239Q8×C43—41no—
240Q8×C43—41no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43#12112yes—
269C2×C4×C43#12112yes—
270C2×C4×C43AGL(1,ℤ/8)12yes—
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×C4×C43H(5,𝔽2)11yescharacteristic
276C2×C4×C432−1+411yescharacteristic
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283D172—41no—
284D172—41no—
285D172—41no—
286D172—41no—
287D172—41no—
288D172—41no—
289D172—41no—
290D172—41no—
291D172—84no—
292D172—84no—
293C43⋊C8—22no—
294C43⋊C8—22no—
295C43⋊C8—22no—
296C43⋊C8—41no—
297#25310—431nomaximal, Sylow
298C22×C43C2×#12111yescharacteristic
299C22×C43#54811yescharacteristic
300C22×C43#55011yescharacteristic
301C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C43#57511yescharacteristic
303C22×C43#57711yescharacteristic
304C22×C43#57711yescharacteristic
305C2×D43—81no—
306C2×D43—81no—
307C2×D43—81no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—81no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C2×D43—81no—
319C4×C43—22no—
320C4×C43—22no—
321C4×C43—22no—
322C4×C43—42no—
323C4×C43—41no—
324C4×C43—41no—
325C4×C43—41no—
326C4×C43—81no—
327C4×C43—81no—
328C4×C43—81no—
329C4×C43#52911yescharacteristic
330C4×C43#54211yescharacteristic
331C4×C43#54611yescharacteristic
332C4×C43#54811yescharacteristic
333Dic43—81no—
334Dic43—81no—
335C2×#460—431no—
336C2×#446—431no—
337#2581D4311yescharacteristic, complemented
338#2548—431no—
339#2067—431no—
340#2065—431no—
341#2055—431no—
342#2055—431no—
343#1973—431no—
344#1968—431no—
345#1961—431no—
346#1949—431no—
347#1936—431no—
348#1934—431no—
349#1763—431no—
350C2×C43#242611yescharacteristic
351C2×C43#305511yescharacteristic
352C2×C43#305711yescharacteristic
353C2×C43#336811yescharacteristic
354C2×C43#337111yescharacteristic
355C2×C43#339711yescharacteristic
356C2×C43#340111yescharacteristic
357D43—161no—
358D43—161no—
359C22×SD16—431no—
360C22×SD16—431no—
361C2×#127—431no—
362C2×#124—861no—
363C2×C4×Q8C2×D4311yescharacteristic
364C2×C4×Q8C2×D4311yescharacteristic
365#460—864no—
366#446—864no—
367C2×#107—431no—
368C2×#106—431no—
369C2×C4⋊C8—431no—
370C2×C4⋊C8—431no—
371C2×C4⋊C8—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#102—431no—
375C2×#102—431no—
376C2×#102—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#97—431no—
381C2×#97—431no—
382C2×C4×C8—431no—
383#400—21no—
384#395—21no—
385#394—861no—
386#394—861no—
387#391C2×D4311yescharacteristic
388#391C2×D4311yescharacteristic
389#390—431no—
390#390—431no—
391#390—431no—
392#390—431no—
393#390—861no—
394#389C2×D4311yescharacteristic
395#389C2×D4311yescharacteristic
396#387—21no—
397#387—21no—
398#382C2×D4311yescharacteristic
399C4×C4⋊C4—431no—
400#340—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404C43#2531011yescharacteristic, complemented, Sylow
405C22×Q8C22⋊D4311yescharacteristic
406C22×Q8C22×D4311yescharacteristic
407C22×D4—431no—
408C22×D4—431no—
409C22×D4—861no—
410C22×D4—861no—
411C2×SD16—862no—
412C2×SD16—862no—
413C2×SD16—862no—
414C2×SD16—862no—
415C2×SD16—1721no—
416C2×SD16—1721no—
417C22×C8—431no—
418C22×C8—431no—
419C22×C8—431no—
420C22×C8—431no—
421#127—862no—
422#127—862no—
423#124—1724no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—431no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4C22⋊D4311yescharacteristic
434C2×C4⋊C4C22⋊D4311yescharacteristic
435C2×C4⋊C4C22⋊D4311yescharacteristic
436C2×C4⋊C4C22×D4311yescharacteristic
437C2×C4⋊C4C22×D4311yescharacteristic
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C22⋊C4—861no—
442C2×C22⋊C4—861no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C22⋊C4—861no—
447C2×C42—21no—
448C2×C42—861no—
449C2×C42C22×D4311yescharacteristic
450C2×C42C22×D4311yescharacteristic
451C2×C42C22×D4311yescharacteristic
452#107—1721no—
453#106—1721no—
454C4⋊C8—434no—
455C4⋊C8—862no—
456C4⋊C8—862no—
457#103—862no—
458#103—862no—
459#102—862no—
460#102—862no—
461#102—862no—
462#102—862no—
463#102—1721no—
464#102—1721no—
465#97—862no—
466#97—862no—
467C4×C8—862no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—861no—
477C24—861no—
478C24—861no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—41no—
487C2×Q8#1062190212yes—
488C2×D4—861no—
489C2×D4—861no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—3441no—
501C2×D4—3441no—
502C2×D4—1722no—
503C2×D4—1722no—
504C2×D4—1722no—
505C2×D4—1722no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4C2×C22⋊D4311yescharacteristic
513C22×C4C2×C22⋊D4311yescharacteristic
514C22×C4C2×C22⋊D4311yescharacteristic
515C22×C4C2×C22⋊D4311yescharacteristic
516C22×C4C2×C22⋊D4311yescharacteristic
517C22×C4C2×C22⋊D4311yescharacteristic
518C22×C4C23×D4311yescharacteristic
519SD16—1724no—
520SD16—1724no—
521C2×C8—432no—
522C2×C8—432no—
523C2×C8—432no—
524C2×C8—861no—
525C2×C8—861no—
526C2×C8—861no—
527C2×C8—861no—
528C2×C8—861no—
529C2×C8—861no—
530C2×C8—861no—
531C2×C8—861no—
532C2×C8—861no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C22⋊C4—3441no—
550C22⋊C4—3441no—
551C22⋊C4—3441no—
552C22⋊C4—3441no—
553C22⋊C4—1722no—
554C22⋊C4—1722no—
555C22⋊C4—1722no—
556C22⋊C4—1722no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—42no—
562C42—1722no—
563C42D4×D4312yes—
564C42#1062190012yes—
565C23—1721no—
566C23—1721no—
567C23—1721no—
568C23—1721no—
569C23—1721no—
570C23—1721no—
571C23—1721no—
572C23—1721no—
573C23—1721no—
574C23—1721no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23C22×C22⋊D4311yescharacteristic
580Q8—22no—
581Q8—22no—
582Q8—44no—
583Q8—41no—
584Q8—41no—
585D4—3444no—
586D4—3444no—
587D4—1721no—
588D4—1721no—
589D4—1721no—
590D4—1721no—
591D4—1721no—
592D4—1721no—
593D4—1721no—
594D4—1721no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—1721no—
623C2×C4—1721no—
624C2×C4—1721no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4#1306329712yes—
629C2×C4#1306329712yes—
630C2×C4#1306335012yes—
631C2×C4C2×D4×D4311yescharacteristic
632C2×C4#41×D4311yescharacteristic
633C2×C4C2×#1062190011yescharacteristic
634C2×C4C2×#1062190211yescharacteristic
635C2×C4#1306337111yescharacteristic
636C2×C4#1306337311yescharacteristic
637C8—862no—
638C8—862no—
639C8—862no—
640C8—1721no—
641C22—3441no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—3441no—
646C22—3441no—
647C22—3441no—
648C22—3441no—
649C22—3441no—
650C22—3441no—
651C22—3441no—
652C22—3441no—
653C22—3441no—
654C22—3441no—
655C22C2×#1306329711yescharacteristic
656C22#1458356011yescharacteristic
657C22#1458356811yescharacteristic
658C22C2×#1306335011yescharacteristic
659C22#1458369711yescharacteristic
660C22#1458370711yescharacteristic
661C22#1458370711yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—42no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—3441no—
673C4—3441no—
674C4#1458343511yescharacteristic
675C4#1458352211yescharacteristic
676C4#1458354011yescharacteristic
677C4#1458355911yescharacteristic
678C2—6881no—
679C2—6881no—
680C2#1913816311yescharacteristic
681C2#1914421611yescharacteristic
682C2#1914423611yescharacteristic
683C2#1914732411yescharacteristic
684C2#1914736311yescharacteristic
685C2#1914761511yescharacteristic
686C2#1914766111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2581C2
socleC23×C43C22×D4
prime radicalC2×#13063322C22
hypercenter#2581D43
hypocenterC43#25310
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2581

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#14583030C2semidirect
4. #19135980C2semidirect
5. #19135966C2semidirect
6. #19135910C2semidirect
7. #19135910C2semidirect
8. #19135479C2semidirect
9. #19135452C2semidirect
11. #19135361C2semidirect
12. #19135291C2semidirect
13. #19135277C2semidirect
14. #19134425C2semidirect
15. C43×#2581C2semidirect
337. #2581D43semidirect
404. C43#25310semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#145830992
C2×#145830302
#191395942
#191359802
#191359662
#191359102
#191354792
#191354522
#191354182
#191353612
#191352912
#191352772
#191344252
C43×#25812
#2531043